2022/02/08 by Quancheng Liu, Liu, Quancheng, David A. Kessler +3 · 1 citation
Computer Science · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum-Dot Cellular Automata #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2202.03640
openalex publication_date 2022/02/08 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28
Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent graphs that can naturally boost target searches. We show how to construct walks with the property that all the eigenvalues of the non-Hermitian survival operator, describing the mixed effects of unitary dynamics and the back-action of measurement, coalesce to zero, corresponding to an exceptional point whose degree is the size of the system. Generally, the resulting search is guaranteed to succeed in a bounded time for any initial condition, which is faster than classical random walks or quantum walks on typical graphs. We then show how this efficient quantum search is related to a quantized topological winding number and further discuss the connection of the problem to an effective massless Dirac particle.